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IOSR Journal of Applied Physics (IOSR-JAP)
e-ISSN: 2278-4861.Volume 7, Issue 5 Ver. I (Sep. - Oct. 2015), PP 107-114
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Laws of High Energy Particle Dynamics
Ravindra D. Rasal1
1
(Maharaja RanjitSingh International Institute, Nanded, Maharashtra, INDIA)
Abstract : Though relativity and quantum mechanics are born out of inadequacies of Newton’s laws, it is yet
possible that Newtonian terms may be used, with appropriate modifications in their meaning for formulation of
the dynamics of high energy- high speed micro particles. Besides three laws on the lines of Newton’s laws a
Forth law is also proposed which radically differs from the aspects of Relativity and Quantum mechanics.
Possibility of creation of particles even without collision like of protons in Large Hadron Collider of CERN is
predicted as a consequence of this formulation.
Keywords - Evolutionary inertia, Threshold velocity, Latent energy, Angel particles, Saturation, Neutrino mass
matrix
I.
INTRODUCTION
Newton’s laws of particle dynamics though do not apply to the dynamics of high energy microparticles yet they provide guidelines for formulating laws for dynamics of high energy particle in context of
recent scientific and technological advancements. The terms used by Newton in his formulation are still useful
by attaching new meanings to them. The relativistic kinetic energy T of a particle with rest mass m0 increases
enormously when u approaches c the rise thus obtained is tabulated in Appendix and illustrated in Fig-1. It was
not possible at the time of inception of Theory of Relativity to impart such high energy to a particle so that its
speed could rise more than 0.9999c which is now achievable in Large Hadron Collider of CERN [1].
Figure 1 : Variation of Kinetic Energy with rising speed.
Data is tabulated in Appendix.
(Graphical Illustration by Dr. Neeraj Anant Pande, Yeshwant Mahavidyalaya (College), Nanded, INDIA)




1

2 
Where T  m0 c 
 1
2
 1  u 

 


c




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Laws of High Energy Particle Dynamics
Had there been no natural barrier, for particles, having mass, to attain the speed of light; they would
then have reached it; that does not happen so due to an obstacle by nature that prevents a mass to reach speed
of light even on imposition of very high energy.
II.
LHC AND INELASTIC COLLISIONS
2.1.
There are certainly similarities between GEDANKEN experiment imagined for deriving
E=mc2 and the actual experimentation in Large Hadron Collider of CERN; but the major difference is that the
colliding particles in GEDANKEN experiment were not having any charge while the collision experiments
in LHC are being conducted with protons.
The combined body formed after collision in LHC is an immense unstable fireball that dissipates into
particles. This fireball contains much more high energy than what would have been obtained by converting
entire mass of colliding particles into energy. In actual collisions only a certain fraction of the energy is
available for conversion into the immense fireballs from which very heavy and unstable particles can be
born [2].
The GEDANKEN experiment, of Einstein‟s era is re-thought in terms of a collision of two identical
masses having no charge at speed comparable with the speed of light.
In the modified GEDANKEN experiment, proposed in this paper in context with the findings of LHC,
a combined body [3] is expected to be formed, same as the “heavy and unstable fireballs” observed,
immediately after inelastic collision in case of collision of protons in LHC.
2.2.
Kinetic Energy of the bodies remains constant in elastic collisions while in inelastic collisions
all the kinetic energy disappears on collision. In its place, after the collision, there appears some form of
internal energy, such as heat energy or excitation energy. Founders of relativity expressed views about
conversion of excess of energy into forms, other than kinetic energy [4], [5], [6], [7].
We now see that this extra internal energy results in rest mass (inertia) of the combined body
being greater than the total rest mass (inertia) of the two separate bodies. Thus the rest mass is equivalent to
energy (rest-mass energy) and must be included in applying the conservation of energy principle. This
result follows from Lorentz transformation and the conservation of momentum principle which were used in
arriving at it [8].
Some type of internal-inertial energy and a force responsible for not allowing masses to reach the
speed of light has been conceived since the very inception of the Special Theory of Relativity. There was,
however, no role of its effect at that time when artificially achievable velocities of objects were much less than
c.
III.
HYPOTHESIS
3.1.
Basis of hypothesis are the objections raised after Einstein‟s Special Theory of Relativity
about quantitative value of speed of light irrespective of its central role in physics .Recent observations on
reminiscent of Big Bang and primordial radiations are tending to conclude that the properties of free space
would also have been different in remote past, so that the value of c would be changing during the course of
cosmological evolution [9]. It was probably very high in inflationary stage of expansion of the universe which
is now decreased to its present value. In view of strong dependence and close relation between velocity of light
and stage of evolution of the universe, “c” is assumed to be a “Stage Constant” [10] related to evolution
meaning that magnitude of c would change, maintaining its central role, during evolution.
3.2.
It would be relevant to use the terms from Newtonian mechanics, in different context for high
energy particles. A new term “evolutionary inertia” is introduced here which means a property of matter which
tries to maintain its stage of evolution. This postulation allows a conservative force that prevents masses to cross
the barrier of c.
3.3
Nature of “evolutionary inertia” hypothesised here can be further explained on the background
of recent developments, like creation of bosons after certain threshold; so that the evolutionary inertia would
be effectively operative after attaining this threshold speed by the particle.
3.4.
The masses which are accelerated to high velocities, approaching speed of light, in proposed
(modified) GEDANKEN experiment; though may be able to acquire very high energy and speed, yet instead of
overtaking the speed of light, they store the energy in a latent form which is converted into particles after
attaining threshold limit or by collision. This latent form of energy resembles the strain energy accumulated in
rocks ahead of rupture which causes earthquake [11].
3.5.
Momentum of any matter-particle is not allowed, by nature, to exceed a certain limit so that
its speed should not increase above c. It is for that matter essential that the particle would itself start creating
new particles, so that the velocity of any of the individual particle should not exceed c. similar to the composite
particles constituted by clamping of quarks and gluons in LHC [12].
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Laws of High Energy Particle Dynamics
3.6.
The force responsible thus for breaking of the particle need not only be an external force but it
could also be an internal property of matter. This is due to a different mode of utilization of energy in high
energy particle physics rather than its simple utilization for accelerating the particle.
3.7.
The creation of new particles can also be visualized in context of Newton‟s third law,
identifying work done against evolutionary inertia as an “action” by the force which tries to accelerate it beyond
speed of light that is opposed by a reaction by creating new particles. Newly created individual particles have
velocities, may even be less than the threshold so as to conserve momentum and energy.
3.8.
There is, however, no analogue for the variety in newly created particles. It is suggested that
this variety is due to an internal or in-built programme of evolution from within the matter that would lead to
an addition of “programme carrying particles” like the so called “Force Carriers” γ, g, z, W in Murray Gell
Mann‟s Standard Model of particles.
3.9.
Stem cell, which is capable of transforming itself into various types of cells leading ultimately
to a programme for formation of different tissues & organs, happens to be well-known biological analogue of
the proposed variety of particles.
Some process like throwing a stone from sling or firing a bullet from gun could be happening on large
scale in the distant celestial bodies, say during supernova explosions, so as to accelerate and emit even
uncharged particles nearly to the speed of light of that era. Postulates of Special Theory of Relativity are thus
modified in the context of results obtained from Large Hydron Collider. Though technology for accelerating
uncharged particles to high velocities, conceived in GEDANKEN experiment, is not yet developed, we are
now able to detect high speed uncharged particles like neutrinos. They appear to be on the verge of crossing
the limit of speed of light [13].
IV.
CREATION OF MATTER OUT OF ENERGY
All the work done by the force F1 acting upon a particle, according to Special Theory of Relativity,
goes into Kinetic Energy and is utilized for accelerating the particle, which increases its velocity to u so that
u u
d
dx
2
u 0 F1dx   dt (mu)dx   d (mu) dt   (mudu  u dm)
from which we obtain relation for variation of mass with energy as
, Yielding to Relativistic
m
m
0
u
1  
c
Kinetic Energy as




1


m0 c 2 
 1
2
u
 1  

 


c


2
and Total Energy E=mc2.
These relations, according to the hypothesis of the present paper, are valid up to the threshold speed
u T.
The threshold speed, which might be characteristic of the object under consideration, is also
hypothecated as a limit, after crossing of which the external force imposed upon the accelerated particle, instead
of contributing totally to acceleration, is utilized partially for creating new particles of matter for which
energy is stored in it in a latent form, that is utilized for creation of matter out of energy.
The Einsteinian equivalence
Total Energy = Relativistic kinetic energy (T) + Rest mass energy
is valid only upto the threshold limit of speed, which may be represented as




1


E  m0 c 2 
 1  m0 c 2  mc 2 , where uT is the threshold speed.
2
u  uT
 uT 


 1   c 



In view of variation of Kinetic Energy T with increase in speed, the threshold may be anticipated to be
somewhere above 0.9c.
Unlike in the Special Theory of Relativity, the particle, after having had achieved a threshold velocity,
would start experiencing the hypothesised “Evolutionary Inertia” so that all the energy imposed upon the
particle would not be fully utilized to accelerate it but a part of it is accumulated in a latent form which is
utilized thereafter for creation of new particles. It is further assumed that the accelerating force is capable to
increase the velocity of particle up to a saturation limit us. The accelerating energy, which is predominant
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Laws of High Energy Particle Dynamics
before achieving threshold, ultimately tends to zero while all the excess of imparted energy becomes creative,
which is represented as
work done
work done in
total
kinetic energy
against evolutionary
convertion of
energy =. used for raising 

inertia to raise the
excess of energy
imparted
velocity upto uT
velocity beyond uT upto us
into particles
E  TuT 
us
d

 F du    dt p 
2
uT
j
j
Where p1=v1m1, p2=v2m2, p3=v3m3, ... are the momenta of newly created particles of which velocities
are individually < c or more often < uT. The particle, in this case, is allowed to be accelerated to saturation limit.
Work done by the force F2 acting upon a particle partially goes into Kinetic Energy and partially
stored into it, in latent form which thereafter, is used for creating new particles. This qualitative change in
mode of utilization of imposed energy is hypothesized due to evolutionary inertia and represented by ∑
instead of ∫ as integration, by definition, is a limit of sum. The above expression is analogues to the process in
which a quantum mechanical function has a range of both continuous and discrete eigenvalues [14]
[15].Integration part of it represents utilization of energy for accelerating the particle while summation indicates
creation of new particles. Proton in Large Hadron Collider, however, does not appear to be accelerated to the
limiting speed us but it is intercepted by collision with the other proton at a speed uʹ so as to be fragmented into
debris. In case if the saturation limit is achieved before collision, then the proton would have had started
acting as a perfect converter of supplied excess energy into particles.
composit 
u'
d 


 Tu   F2 du   unstable  =   p  .

E
 dt  j
j
inelastic &
u
 matter 
premature
T
T
collision
Where uT < u‟ < us.
Collision in LHC may also be conceived as a premature trigger.
V.
SEISMOLOGICAL ANALOGY AND FLUX OF NEUTRINOS
The latent energy proposed to be accumulated in the particle, is analogous to the strain accumulated in
hard material of tectonic plates of earth. The limit of uT is similar to the elastic limit beyond which strain is not
directly proportional to stress. The name “Angel particles” is proposed by the author for those entities which
are coming out from within the earth before major earthquakes. They are expected to perturb animals, birds and
fishes. These angels resemble neutrinos in their capacity to penetrate hard rock [16].
There is yet another similarity between process of emission of Angel particles ahead of earthquake and
the neutrinos apparently moving at or even more than the speed of light, found in experiments with Large
Hadron Collider. It is the resemblance between seismological stress matrix [17] with the neutrino mass
matrix [18]. Neutrinos may leak through LHC by quantum tunnelling [19], [20] like the flux of Angel particles
through hard crust of earth.
Fig- 2 Particle Creation Scenario at High Energies
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Laws of High Energy Particle Dynamics
VI.
DISCUSSION
6.1
Interaction of bodies is the most frequently observed phenomenon in nature. Direct physical
contact, like that of billiard balls is not always necessary for their interaction. Round trip passage of comet
through solar system [21] or interaction of proton with nucleus are also treated as types of collisions in which
the other forces such as gravity, Coulomb‟s repulsive force, strong sub-nuclear forces are predominant. The
evolutionary inertia is conceived here to be most predominant in the range of velocity approaching the
speed of light.
6.2
Any mechanism, as per the theories about generating elementary particles, must become
active above certain energy level, such as two 3.5 TeV for proton beams colliding in LHC [22] for producing
Higgs particles. This inference is in support of the proposed threshold speed for activation of evolutionary
inertia. This is the energy threshold observed in case of proton in LHC, the other particles may have different
thresholds. The chain begins from formation of Quarks. Quarks make nucleons, and the nucleons make
nuclei. Nuclei and electrons make atoms, molecules and all the known non-living and living matter. [2 3]
6.3
The ideas of threshold velocity and evolutionary inertia are suggested as most probable valid
reasons for creation of new matter. The scope of this paper is limited to the cause of creation of new particles.
Classification and types of created particles, their properties and positions in Standard Model of particles etc.
[24] [25] are beyond the scope of this paper.
6.4
Conversion of excess of energy, into a latent form as the cause of creation of new matter
appears to be more rational explanation than the so called omnipresent Higgs mechanism imparting masses to
various forms of existences and that all known elementary particles remain as mass-less (existences) unless
they interact with Higgs field [26].
6.5
Phenomenon of neutrinos moving at speed of light or appearing to move even faster than
that of light, detected by ICARUS from CERN [27] was an international news on 23rd September 2011. It
could be “leakage” of neutrinos probably due to quantum tunnelling. Stream of such neutrinos could also
emerge out of supernova explosion from the matter in an ancient stage of evolution. Antonio Ereditato claimed
that ancient neutrinos from supernova explosion, which was first noticed in 1987 preceded light by few hours in
reaching the earth [28]. Such neutrinos can thus be believed to have tunnelled [29] across the then speed limit
(of light) that could be higher than its present value.
6.6.
Flux of superluminal neutrinos from supernova itself is yet another evidence for higher value
of c in remote past. This is what is defined as Relativity of stages of evolution [30] by the author.
The supernova might have naturally accelerated charge-less particles to a velocity very near to the then
speed of light.
6.7.
Spontaneous breaking of an underlying symmetry according to presently accepted theories,
is said to be the cause of birth of massive particles [31], [32]. It does not, however, provide any answer as to
„where from‟, „how‟ and „why‟ this spontaneity comes? It is suggested that the spontaneity is an outcome of an
internal urge of matter for evolution.
VII.
CONCLUSION
Inference from experiments of Collision in Large Hadron Collider means only that a new particle is
found. Its identity with predicted Higgs boson does not justify the Higgs mechanism. An alternative mode, as
suggested by the author in this paper can also be the cause of creation of new particle. There is every possibility
that the hypothesis of this paper would be verified by observing creation of particles together with dissipation
of energy into particles before collision in LHC.
Certain laws for dynamics of high energy particles are formulated on the basis of above, which are as
under:
1st Law of High Energy Particle Dynamics :- Every moving particle continues in its stage of
evolution, so far as it be accelerated to a limit of velocity by an external-impressed force due to a type of inertia
defined as evolutionary inertia.
2nd Law of High Energy Particle Dynamics :- A natural force becomes effective, after crossing a
limit of speed that constraints the momentum of moving particle so as not to cross the speed of light. The force,
thereafter, yield a new type of energy which generates matter-particles out of energy.
3rd Law of High Energy Particle Dynamics:- The action of imposed force on the particle to
accelerate it is countered by a reaction which after a certain limit results into creation of particles.
4th Law of High Energy Particle Dynamics :- The energy, in itself, contains an in-built programme of
evolution that imparts variety into created particles of matter, during collision or dissipation.
The programme is analogous to primitive form of molecular mechanism of inheritance. It may be
narrated in a Sanskrit verse as Eko’ haṁbahusyām [33] meaning “I am one, would like to be many”.
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Laws of High Energy Particle Dynamics
Acknowledgements
Author is thankful to Prof. Dr. Neeraj Anant Pande from Mathematics Dept. of Yeshwant
Mahavidyalaya (College), Nanded, Principal (retd.) Dr.Omprakash Rathod of Science College, Nanded, Prof.
Dr.Rajendra Khairnar from Physics Dept of SRTM University, Nanded, Prof. Dr .Manish Deshpande from
Physics Dept of NSB College, Nanded and Mr.M.A.Khan for their valuable assistance in preparing this paper.
REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
[22]
[23]
[24]
[25]
[26]
[27]
[28]
[29]
[30]
[31]
[32]
[33]
Binay Malakar, Search for the Higgs Boson, Science Reporter (NISCAIR) CSIR, New Delhi, 49(7), July 2012, 12.
B. Ananthanarayan, Anant, The Discovery of the Higgs Particle, Current Science, 103(1), 2012, 16-18.
Robert Resnick, Special Relativity (Wiley Eastern, 14th reprint 1990), Fig 3-7, 131.
Albert Einstein, Meaning of Relativity (Oxford & IBH, Indian Edition 1965), 45.
W.Rindler, Special Relativity (Oliver & Boyd, 1960), 73.
Irving Kaplan, Nuclear Physics (Addison-Wesley/Narosa 2nd Ed.1987), 489.
A.N.Matveev, Mechanics & Theory of Relativity (Mir Moscow, 1989), 181.
Robert Resnick, Special Relativity (Wiley Eastern, 14th reprint 1990), 131.
Ravindra D.Rasal, Alternative to Doppler Effect for Red Shift in Case of Long distant Celestial Objects, IOSR Journal of Physics,
7(2), 51-53.
Ravindra D.Rasal, Explanation for Superluminal Motion Observed in Large Hadron Collider, paper presented at 77th Annual
Conference of Indian Mathematical Society, Swami Ramanand Teerth Marathwada University, Nanded, 27-30th December 2011, P76 of Abstracts Book. This paper was based on EPISTEMIC LORENTZ TRANSFORMATION; Ref. Evolutionary Approach to
Relativity, 1994, Laxminarayan Pub. Opp. Collector‟s Office, near Railway Station PARBHANI 431401, p- 105.
William Lowrie, Fundamentals of Geophysics (Cambridge Univ. Press, 1997), 110.
Zvi Bern, Lance J.Dixon & David Kosower, On a Sunny Spring Day, Scientific American, USA, May 2012, 36-41.
M.Antonello et el, Measurement of neutrino velocity with ICARUS detector at CNGS Beam, arXiv:1203.3433v3[hep-ex], 29 Mar
2012, also M.Antonello Wikipedia, http://en.wikipedia.org/wiki/Higgs_boson 16/12/2011.
Robert Dicke & James Wittke, Quantum Mechanics (Addison-Wesley, 1970), 99.
Louis A.Pipes, Applied Mathematics (McGraw-Hill, 2nd Ed.1958), 517.
Ravindra D.Rasal, Intimation of Earthquake by Angel Particles, 102nd Indian Science Congress , University of Mumbai, 3-7 January
2015, p157, Available on the blog ravindrarasal.wordpress.com.
William Lowrie, Fundamentals of Geophysics (Cambridge Univ. Press, 1997), 86.
Beyond Standard Model, Proceedings-415 of 5th Conference of American Institute of Physics , p306.
Robert Dicke & James Wittke, Quantum Mechanics (Addison-Wesley, 1970), 41.
David Bohm, Quantum Mechanics, 275.
A.N.Matveev, Mechanics & Theory of Relativity (Mir Moscow, 1989), 279.
Prafulla Kumar Behera, Discovery of SM Higgs Boson in ATLAS Experiment, Resonance, March 2013, 248-263 (energy threshold
p-256).
G.Rajasekaran, Standard Model, Higgs Boson and What Next?, Resonance, October 2012, 965.
G.Rajasekaran, Standard Model, Higgs Boson and What Next?, Resonance, October 2012, 961.
David Griffiths, Introduction to Elementary Particles (John Wiley & Sons, 1987), 321,322,325,351,365.
B. Ananthanarayan, Anant, The Discovery of the Higgs Particle, Current Science, 103(1), 2012, 16-18.
M.Antonello et el, Measurement of neutrino velocity with ICARUS detector at CNGS Beam, arXiv:1203.3433v3[hep-ex], 29 Mar
2012.
Antonio Ereditato, An Interview with Antonio Ereditato by Atul Thakur, Sunday Review, The Times of India, 06th Feb 2011.
Ravindra D.Rasal, Alternative to Doppler Effect for Red Shift in Case of Long distant Celestial Objects, IOSR Journal of Physics,
7(2), 51-53.
Ravindra D.Rasal, Evolutionary Approach to Relativity (Laxminarayan Pub. Opp. Collector‟s Office, near Railway Station,
Parbhani 431401, India), 76, 93.
Gangan B.Mohanty, Discovery of a Boson at CERN and Indian Connections Resonance, March 2013, 241.
B. Ananthanarayan, Anant, The Discovery of the Higgs Particle, Current Science, 103(1), 2012, 17.
Apaurusheya, Chandogya Upanished (6.2.1-3) Sanskrit Hindu Scripture, 8th to 6th Century BC.
APPENDIX
u
c
T

m0 c 2
1
u
1  
c
0.866
0.99982402
0.867
1.00679043
0.880
1.10537980
0.891
1.20262714
0.900
1.29415734
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2
1
112 | Page
Laws of High Energy Particle Dynamics
u
c
T

m0 c 2
1
u
1  
c
2
0.901
1.30510835
0.910
1.41191535
0.917
1.50697439
0.923
1.59875295
0.924
1.61511427
0.929
1.70212050
0.935
1.81969956
0.939
1.90767711
0.943
2.00487335
0.959
2.52850595
0.969
3.04758796
0.979
3.90532126
0.980
4.02518908
0.987
5.22199117
0.990
6.08881205
0.993
7.46637168
0.994
8.14243324
0.995
9.01252349
0.996
10.19153703
0.997
11.91963785
0.998
14.81929993
0.999
21.36627204
0.9999
69.71244595
0.99999
222.60735677
0.999999
706.10695807
0.9999999
2,235.06803643
0.99999999
7,070.06793148
0.999999999
22,359.68257373
0.9999999999
70,709.75369809
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1
113 | Page
Laws of High Energy Particle Dynamics
u
c
T

m0 c 2
1
u
1  
c
2
1
0.99999999999
223,608.27107451
0.999999999999
707,192.12283025
0.9999999999999
2,238,204.92666454
0.99999999999999
7,153,827.93930562
0.999999999999999
25,364,765.41600790
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